Just as the absence of lines of fixation results in the lack of the required succession of the local signs, so in a sigular manner the sensations of conference connected with movement, are absent in rigid fixation. c. Relations between the Location of the Elements in regard to one another and the Location in Regard to the Subject.
31. When the field of vision is thought of as merely a location of impressions in relation to one another, we represent it to ourselves is a surface, and call the single ob- [p. 137] jects lying in this surface ideas of two dimensions, in contrast to the ideas of depth. But even an idea of two dimensions must always be related to the seeing subject in two ways.
First, every point in the field of vision is seen ill a particular direction on the subjective line of orientation mentioned above (p. 131). Secondly, the whole field of vision is localized at some distance or other from the subject, though this distance may be very indefinite.
The location in a particular direction results in an erect ideational object corresponding to an inverted retinal image. This relation between the objective localization in direction and the retinal image is as necessary a result of ocular movements as the inversion of the image itself is a result of the optical properties of the eye. Our line of orientation in space is the external line of regard or, for binocular vision, the middle line resulting from the combined effects of movements of fixation.
A direction upward on this line of orientation in external space corresponds to a direction downward in the space where the retinal image lies, behind the centre of ocular rotation, and vice versa. It follows that the retinal image must be inverted if we are to see the object erect.
32. The location at some distance or other, which is also never absent, brings about the result that all the points of the field of vision seem to be arranged on the surface of a concave hemisphere whose centre is the point of orientation, or, in monocular vision, the point of the eye's rotation. Now, small areas of a large curved surface appear plane, so that the two-dimensional ideas of single objects are as a rule plane; thus, for example, figures drawn upon t plane, as those of plane geometry.
But as soon as some parts of the general field of vision separate from it in such a way that they are localized before or behind, that is in different planes, the idea of two dimensions gives place to one of three. [p. 138]
32 a. The fusions formed between qualitative local signs and sensations of convergence when we change from the fixation of a more distant point to a nearer, or the reverse, may be called complex local signs of depth. Such local signs form for every series of points lying before or behind the fixation-point, or for an extended body which is nothing but a series of such points, a regularly arranged system in which a stereometric form located at a particular distance is always unequivocally represented by a particular fusion. When one of two points lying at different distances is fixated, the other is characterized by the different position of its images in the two eyes, and by the correspondingly different direction of the complex local signs in the two cases. The same is true for connected series of points or extended bodies. When we look at a solid object, it throws images in the two eyes that are different from each other on account of the different relative position of the object with regard to the two eyes. We may designate the difference between the positions of certain point in the image in the two eyes as the binocularparallax. This parallax is zero for the point fixated and for those points which are equally distant on the line of orientation; for all other points it has some real positive or negative value accordingly, as they are more or less distant than the fixation-point. If we fixate solid objects with both eyes, only the point fixated, together with those points which are equidistant and in its neighborhood in the field of vision, will give rise to images corresponding in position in the two eyes. All points of the object located at different distances, give images varying in position and size. These differences in the images are just what produce the idea of the solidity of the object when the proper lines of fixation are present. For in the way above described, the angle of binocular parallax for the image of any point lying before or behind the point of fixation and connected with the same by a line of fixation, furnishes, according to its direction and magnitude, a measure for the relative distance of this point in depth through the complex local signs connected with the angle of parallax. This angle of parallax for a given objective depth, decreases proportionally to the distance of the solid object, so that the impression of solidity diminishes, the further of the objects are, and when the distance is so great that all angles of parallax [p. 139] disappear, the body will appear flat, unless the associations to be discussed later (§ 16, 9) produce an idea of depth.
33. The influence of binocular vision on the idea of depth may be investigated experimentally by means of a stereoscope . This instrument consists of two prisms with their angles of refraction turned toward each other in such a way that it renders possible a binocular combination of two plain drawings which correspond to the retinal images from a three-dimensional object. The influence of the various conditions that underlie the formation of ideas of depths, may, in this way, be studied much better than by looking at actual three-dimensional objects, for here we may vary the conditions at will.